In the selection and debugging of the servo system, inertia problems are often encountered. Its specific performance is:

When selecting the servo system, in addition to considering factors such as the torque and rated speed of the motor, we also need to calculate the inertia converted to the motor shaft by the mechanical system, and then specify the actual motion requirements of the machine and the quality requirements of the processed parts. Select a motor with a suitable inertia size; when debugging, correctly setting the inertia ratio parameter is a prerequisite for giving full play to the best performance of the mechanical and servo system. This point is particularly prominent in systems that require high speed and high precision. In this way, there is the problem of inertia matching.

### 1. What is “inertia matching”?

1. According to Newton’s second law: “The required torque T of the feed system = the system transmission inertia J × the angular acceleration θ angle”. The acceleration θ affects the dynamic characteristics of the system. The smaller the θ, the longer the time from when the controller sends an instruction to the completion of the system execution, and the slower the system response. If θ changes, the system will react quickly and slowly, which will affect the processing accuracy. Since the maximum output T value remains unchanged after the motor is selected, if the change in θ is desired to be small, then J should be as small as possible.

2. The total inertia of the feed axis “J = the rotational inertia momentum of the servo motor JM + the load inertia momentum JL converted by the motor shaft. The load inertia JL is determined by the workbench and the fixtures and workpieces mounted ON it (take a plane metal cutting machine as an example) The inertia of Linear and rotary moving parts such as, screw, coupling, etc. is converted to the inertia of the motor shaft. JM is the rotor inertia of the servo motor. After the servo motor is selected, this value is a fixed value, while JL varies with the load such as the workpiece Change and change. If you want a smaller rate of change of J, it is better to make the proportion of JL smaller. This is the “inertia matching” in the popular sense.

### 2. How to determine “inertia matching”?

The transmission inertia has an impact on the accuracy, stability and dynamic response of the servo system. The inertia is large, the mechanical constant of the system is large, and the response is slow, which will reduce the natural frequency of the system and easily produce resonance, which limits the servo bandwidth and affects the servo accuracy and response speed. An appropriate increase in inertia is only beneficial when improving low-speed crawling. Therefore, the inertia should be reduced as much as possible when the mechanical design does not affect the rigidity of the system.

When measuring the dynamic characteristics of a mechanical system, the smaller the inertia, the better the response of the system’s dynamic characteristics; the greater the inertia, the greater the load of the motor and the more difficult it is to control, but the inertia of the mechanical system must match the inertia of the motor. Different institutions have different choices for the principle of inertia matching and have different performances. Different mechanism actions and processing quality requirements have different requirements for the relationship between JL and JM, but most require the ratio of JL to JM to be less than ten. In a word, the determination of inertia matching needs to be determined according to the technological characteristics and processing quality requirements of the machine. For basic metal cutting machine tools, for servo motors, it is generally recommended that the load inertia should be less than 5 times the motor inertia.

Inertia matching is very important for motor selection. For motors of the same power, some brands have light inertia, medium inertia, or large inertia. In fact, the load inertia is best calculated by formula. Common formulas for calculating the inertia of the body are readily available in the books previously studied (you can check the mechanical design manual). We once did an experiment where a large inertia disk was added to the shaft extension of a servo motor to be used for testing. The result was that the servo motor couldn’t stop at low speed, shook its head and shook its tail, and couldn’t stop oscillating. Later, it was changed to: install a coupling on the shaft extensions of the two servo motors, and energize one of the servo motors as the driving force, and the other servo motor as the slave, that is, as a small load. It turns out that the swaying servo motor starts, moves, stops, and everything runs normally!

### Three, the theoretical calculation formula of inertia

Inertia calculations have formulas. As for multiple loads, such as gears with gears, or worm gear drives, as long as the inertia of each rotating part is calculated separately and then added, it is the system inertia. When selecting the motor, it is recommended to select different motors. The moment of inertia of the load must be calculated through calculations during design. If there is no such value, the motor selection must be unreasonable, or there will definitely be problems. This is one of the most important parameters for selecting the servo. . As for the motor inertia, it is marked in the motor sample manual. Of course, for some servos, the inertia of the load can be measured through the process of adjusting the servo, which can be used as a reference for calculation in theoretical design. After all, in the design stage, many parameters such as friction coefficient can only be guessed based on experience and cannot be accurate. The calculation formula in the theoretical design: (for reference only) The moment of inertia J is usually expressed by the flywheel moment GD2, and the relationship between them is:

J=mp^2= GD^2/4g

Where m and G-the mass (kg) and weight (N) of the rotating part;

And D-radius and diameter of inertia (m);

g=9.81m/s2-gravitational acceleration

Flywheel inertia = speed change rate * flywheel distance/375

Of course, there will always be deviations between theory and reality. In some regions (such as in Europe), the median value is generally obtained through actual tests. In this way, it is more accurate than our empirical formula. However, it still needs to be calculated at present, and there are also fixed formulas that can be consulted in the mechanical design manual.

### 4. About the friction coefficient?

Regarding the friction coefficient, the general motor selection only considers a coefficient to be added to the calculation process, which is usually not considered when the motor is adjusted. However, if this factor is large, or it is enough to affect the adjustment of the motor, some Japanese general-purpose servos have a parameter that is said to be used for special testing. As for whether it is easy to use, I have not used it, and it is estimated that it should be easy to use. Some netizens said in a post that someone once happened to copy a foreign machine in the design. The mechanical part is the same, the motor power is amplified by 50%, but the motor can’t rotate. Because the precision of machining and assembly of the prototype is too poor, the load inertia is almost the same, but the friction resistance is too different, and the specific working conditions are not considered properly.

Of course, viscous damping and friction coefficient are not the same problem. The friction coefficient is a constant value, which can be compensated by the motor power, but the viscous damping is a variable value, which can of course be alleviated by increasing the motor power, but it is actually unreasonable. Moreover, there is no design basis. This is best solved in the mechanical state. Without a good mechanical state, the servo adjustment is completely empty talk. In addition, viscous damping is related to mechanical structure design, processing, assembly, etc., which must be considered when selecting models. And it is closely related to the friction coefficient. It is precisely because the processing level is not enough that the friction coefficient is uncertain, and the difference is large, and even the difference in the assembly level of the skilled workers will cause a big difference. These must be necessary in the selection of the motor. considerate. In this way, there will be an insurance factor, of course, in the final analysis, it is still a problem of motor power.

### 5. After the theoretical calculation of inertia, the simplification of fine-tuning and correction

Some friends may think: too complicated! The actual situation is that various parameters of a certain brand’s product have been determined. Under the conditions of power, torque, and speed, the product model has been determined. If the inertia is still not satisfied, can the power be increased by one gear to meet the inertia? Requirements?

The answer is: if the increase in power can lead to an increase in acceleration, it should be possible.

### 6. Servo motor selection

After choosing the mechanical transmission scheme, the model and size of the servo motor must be selected and confirmed.

(1) Selection conditions: Under normal circumstances, the selection of a servo motor must meet the following conditions:

1. The maximum speed of the motor> the maximum moving speed required by the system

2. The rotor inertia of the motor matches the load inertia

3 Continuous load working torque ≤ motor rated torque

4. The maximum output torque of the motor>the maximum torque required by the system (torque during acceleration)

(2) Selection calculation:

Inertia matching calculation (JL/JM)

Rotation speed calculation (load end speed, motor end speed)

Load torque calculation (continuous load working torque, torque during acceleration)